In contradiction to the nature of the spin-orbit driven Rashba splitting of surface states which increases with atomic number, Shikin et al. {[}Phys. Rev. Lett. 100, 057601 (2008)] have observed that the size of the splitting in Au overlayers on W(110) is smaller than for Ag overlayers. In the framework of first-principle density functional theory, we have studied the origin of the Rashba splitting at Au/Ag overlayers on the W(110) surface. We show how the asymmetric behavior of the wave function in the vicinity of the surface atom nucleus, in addition to the strength of the nuclear potential gradient, plays a crucial role for the size of the splitting. The influence of the electronic structure and spin dependent hybridization on the Rashba splitting is discussed. The asymmetric behavior of the surface wave function originates from the surface-interface sp-d hybridization. We find that a spin dependent hybridization in the Ag overlayer influences strongly the size of the Rashba splitting. DOI: 10.1103/PhysRevB.86.235437